The functions given below are the ones which a user of PostGIS Raster is likely to need and which are currently available in PostGIS Raster. There are other functions which are required support functions to the raster objects which are not of use to a general user. raster is a new PostGIS type for storing and analyzing raster data. For more information about Raster, please refer to PostGIS Raster Home Page. For the examples in this reference we will be using a raster table of dummy rasters - Formed with the following code CREATE TABLE dummy_rast(rid integer, rast raster); INSERT INTO dummy_rast(rid, rast) VALUES (1, ('01' -- little endian (uint8 ndr) || '0000' -- version (uint16 0) || '0000' -- nBands (uint16 0) || '0000000000000040' -- scaleX (float64 2) || '0000000000000840' -- scaleY (float64 3) || '000000000000E03F' -- ipX (float64 0.5) || '000000000000E03F' -- ipY (float64 0.5) || '0000000000000000' -- skewX (float64 0) || '0000000000000000' -- skewY (float64 0) || '00000000' -- SRID (int32 0) || '0A00' -- width (uint16 10) || '1400' -- height (uint16 20) )::raster ), -- Raster: 5 x 5 pixels, 3 bands, PT_8BUI pixel type, NODATA = 0 (2, ('01000003009A9999999999A93F9A9999999999A9BF000000E02B274A' || '41000000007719564100000000000000000000000000000000FFFFFFFF050005000400FDFEFDFEFEFDFEFEFDF9FAFEF' || 'EFCF9FBFDFEFEFDFCFAFEFEFE04004E627AADD16076B4F9FE6370A9F5FE59637AB0E54F58617087040046566487A1506CA2E3FA5A6CAFFBFE4D566DA4CB3E454C5665')::raster); AddRasterColumn Adds a raster column to an existing table and generates column constraint on the new column to enforce srid. text AddRasterColumn varchar table_name varchar column_name integer srid varchar[] pixel_types boolean out_db boolean regular_blocking double precision[] no_data_values double precision pixelsize_x double precision pixelsize_y integer blocksize_x integer blocksize_y geometry envelope text AddRasterColumn varchar schema_name varchar table_name varchar column_name integer srid varchar[] pixel_types boolean out_db boolean regular_blocking double precision[] no_data_values double precision pixelsize_x double precision pixelsize_y integer blocksize_x integer blocksize_y geometry envelope text AddRasterColumn varchar catalog_name varchar schema_name varchar table_name varchar column_name integer srid varchar[] pixel_types boolean out_db boolean regular_blocking double precision[] no_data_values double precision pixelsize_x double precision pixelsize_y integer blocksize_x integer blocksize_y geometry envelope Adds a raster column to an existing table and also generates constraints on the new column. Currently only constrains the SRID. The schema_name is the name of the table schema (unused for pre-schema PostgreSQL installations). The srid must be an integer value reference to an entry in the SPATIAL_REF_SYS table. The pixel_types must be an array of pixel types as described in , one for each band. An error is thrown if the schemaname doesn't exist (or not visible in the current search_path) or the specified SRID, pixel types are invalid. gdal2raster.py loader uses this function to register raster tables Views and derivatively created spatial tables will need to be registered in raster_columns manually, since AddRasterColumn also adds a raster column which is not needed when you already have a raster column. SELECT AddRasterColumn('public', 'myrasters', 'rast',4326, '{8BUI,8BUI,8BUI,8BUI}', false, true, '{255,255,255,255}', 0.25,-0.25,200,300, null); public.myrasters.rast srid:4326 pixel_types:{8BUI,8BUI,8BUI,8BUI} out_db:false regular_blocking:true nodata_values:'{255,255,255,255}' pixelsize_x:'0.25' pixelsize_y:'-0.25' blocksize_x:'200' blocksize_y:'300' extent:NULL --- After loading the data, you can currect the geometry column UPDATE raster_columns SET extent = (SELECT ST_Union(ST_Envelope(rast)) FROM myrasters) WHERE r_table_schema = 'public' AND r_table_name = 'myrasters' AND r_column = 'rast'; , , , DropRasterColumn Removes a raster column from a table. text DropRasterColumn varchar table_name varchar column_name text DropRasterColumn varchar schema_name varchar table_name varchar column_name text DropRasterColumn varchar catalog_name varchar schema_name varchar table_name varchar column_name Removes a raster column from a table. Note that schema_name will need to match the r_table_schema field of the table's row in the raster_columns table. SELECT DropRasterColumn ('my_schema','my_raster_table','rast'); ----RESULT output --- my_schema.my_raster_table.rast effectively removed. , DropRasterTable Drops a table and all its references in raster_columns. text DropRasterTable varchar table_name text DropRasterTable varchar schema_name varchar table_name text DropRasterTable varchar catalog_name varchar schema_name varchar table_name Drops a table and all its references in raster_columns. Note: uses current_schema() on schema-aware pgsql installations if schema is not provided. SELECT DropRasterTable ('my_schema','my_raster_table'); ----RESULT output --- my_schema.my_raster_table dropped. , PostGIS_Raster_Lib_Build_Date Reports full raster library build date text PostGIS_Raster_Lib_Build_Date Reports raster build date SELECT PostGIS_Raster_Lib_Build_Date(); postgis_raster_lib_build_date ----------------------------- 2010-04-28 21:15:10 PostGIS_Raster_Lib_Version Reports full raster version and build configuration infos. text PostGIS_Raster_Lib_Version Reports full raster version and build configuration infos. SELECT PostGIS_Raster_Lib_Version(); postgis_raster_lib_version ----------------------------- 0.1.6d ST_MakeEmptyRaster Returns an empty raster of given dimensions, pixel x y, skew and spatial reference system with no bands raster ST_MakeEmptyRaster integer width integer height float8 ipx float8 ipy float8 scalex float8 scaley float8 skewx float8 skewy integer srid Returns an empty raster of given dimensions, pixel x y, skew and spatial reference system with no bands. After you create an empty raster you probably want to add bands to it and hmm maybe edit it. Refer to to define bands and to set pixel values. INSERT INTO dummy_rast(rid,rast) VALUES(3, ST_MakeEmptyRaster( 100, 100, 0.0005, 0.0005, 1, 1, 0, 0, 4326) ) , ST_GeoReference Returns the georeference meta data in GDAL or ESRI format as commonly seen in a world file. Default is GDAL. text ST_GeoReference raster rast text ST_GeoReference raster rast text format Returns the georeference meta data including carriage return in GDAL or ESRI format as commonly seen in a world file. Default is GDAL if no type specified. type is string 'GDAL' or 'ESRI'. Difference between format representations is as follows: GDAL: pixelsizex skewy skewx pixelsizey upperleftx upperlefty ESRI: pixelsizex skewy skewx pixelsizey upperleftx + pixelsizex*0.5 upperlefty + pixelsizey*0.5 SELECT ST_GeoReference(rast, 'ESRI') As esri_ref, ST_GeoReference(rast, 'GDAL') As gdal_ref FROM dummy_rast WHERE rid=1; esri_ref | gdal_ref --------------+-------------- 2.0000000000 | 2.0000000000 0.0000000000 : 0.0000000000 0.0000000000 : 0.0000000000 3.0000000000 : 3.0000000000 1.5000000000 : 0.5000000000 2.0000000000 : 0.5000000000 , , ST_Height Returns the height of the raster in pixels? integer ST_Height raster rast Returns the height of the raster. SELECT rid, ST_Height(rast) As rastheight FROM dummy_rast; rid | rastheight -----+------------ 1 | 20 2 | 5 ST_MetaData Returns basic meta data about a raster object such as skew, rotation, upper,lower left etc. record ST_MetaData raster rast Returns basic meta data about a raster object such as skew, rotation, upper,lower left etc. Columns returned upperleftx | upperlefty | width | height | pixelsizex | pixelsizey | skewx | skewy | srid | numbands SELECT rid, (foo.md).* FROM (SELECT rid, ST_MetaData(rast) As md FROM dummy_rast) As foo; rid | upperleftx | upperlefty | width | height | pixelsizex | pixelsizey | skewx | skewy | srid | numbands -----+------------+------------+-------+--------+-----------+-----------+-------+-------+------+---------- 1 | 0.5 | 0.5 | 10 | 20 | 2 | 3 | 0 | 0 | 0 | 0 2 | 3427927.75 | 5793244 | 5 | 5 | 0.05 | -0.05 | 0 | 0 | -1 | 3 , ST_NumBands Returns the number of bands in the raster object. integer ST_NumBands raster rast Returns the number of bands in the raster object. SELECT rid, ST_NumBands(rast) As numbands FROM dummy_rast; rid | numbands ----+---------- 1 | 0 2 | 3 ST_PixelSizeX Returns the x size of pixels in units of coordinate reference system? float8 ST_PixelSizeX raster rast Returns the x size of pixels in units of coordinate reference system? SELECT rid, ST_PixelSizeX(rast) As rastpixwidth FROM dummy_rast; rid | rastpixwidth -----+-------------- 1 | 2 2 | 0.05 ST_PixelSizeY Returns the y size of pixels in units of coordinate reference system? float8 ST_PixelSizeY raster rast Returns the y size of pixels in units of coordinate reference system. May be negative. Refer to World File for more details. SELECT rid, ST_PixelSizeY(rast) As rastpixheight FROM dummy_rast; rid | rastpixheight -----+--------------- 1 | 3 2 | -0.05 ST_Raster2WorldCoordX Returns the geometric x coordinate upper left of a raster , column and row. Numbering of columns and rows starts at 1. float8 ST_Raster2WorldCoordX raster rast integer xcolumn float8 ST_Raster2WorldCoordX raster rast integer xcolumn integer yrow Returns the upper left x coordinate of a raster column row in geometric units of the georeferenced raster. Numbering of columns and rows starts at 1 but if you pass in a negative number or number higher than number of columns in raster, it will give you coordinates outside of the raster file to left or right with the assumption that the skew and pixel sizes are same as selected raster. For non-skewed rasters, providing the x column is sufficient. For skewed rasters, the georeferenced coordinate is a function of the ST_PixelSizeX and SkewX and row and column. An error will be raised if you give just the x column for a skewed raster. -- non-skewed raster providing column is sufficient SELECT rid, ST_Raster2WorldCoordX(rast,1) As x1coord, ST_Raster2WorldCoordX(rast,2) As x2coord, ST_PixelSizeX(rast) As pixelx FROM dummy_rast; rid | x1coord | x2coord | pixelx -----+------------+-----------+-------- 1 | 0.5 | 2.5 | 2 2 | 3427927.75 | 3427927.8 | 0.05 -- for fun lets skew it SELECT rid, ST_Raster2WorldCoordX(rast,1,1) As x1coord, ST_Raster2WorldCoordX(rast,2,3) As x2coord, ST_PixelSizeX(rast) As pixelx FROM (SELECT rid, ST_SetSkew(rast,100.5,0) As rast FROM dummy_rast) As foo; rid | x1coord | x2coord | pixelx -----+------------+-----------+-------- 1 | 0.5 | 203.5 | 2 2 | 3427927.75 | 3428128.8 | 0.05 , , , ST_Raster2WorldCoordY Returns the geometric y coordinate upper left corner of a raster , column and row. Numbering of columns and rows starts at 1. float8 ST_Raster2WorldCoordY raster rast integer yrow float8 ST_Raster2WorldCoordY raster rast integer xcolumn integer yrow Returns the upper left y coordinate of a raster column row in geometric units of the georeferenced raster. Numbering of columns and rows starts at 1 but if you pass in a negative number or number higher than number of columns/rows in raster, it will give you coordinates outside of the raster file to left or right with the assumption that the skew and pixel sizes are same as selected raster tile. For non-skewed rasters, providing the y column is sufficient. For skewed rasters, the georeferenced coordinate is a function of the ST_PixelSizeY and SkewY and row and column. An error will be raised if you give just the y row for a skewed raster. -- non-skewed raster providing row is sufficient SELECT rid, ST_Raster2WorldCoordY(rast,1) As y1coord, ST_Raster2WorldCoordY(rast,3) As y2coord, ST_PixelSizeY(rast) As pixely FROM dummy_rast; rid | y1coord | y2coord | pixely -----+---------+-----------+-------- 1 | 0.5 | 6.5 | 3 2 | 5793244 | 5793243.9 | -0.05 -- for fun lets skew it SELECT rid, ST_Raster2WorldCoordY(rast,1,1) As y1coord, ST_Raster2WorldCoordY(rast,2,3) As y2coord, ST_PixelSizeY(rast) As pixely FROM (SELECT rid, ST_SetSkew(rast,0,100.5) As rast FROM dummy_rast) As foo; rid | y1coord | y2coord | pixely -----+---------+-----------+-------- 1 | 0.5 | 107 | 3 2 | 5793244 | 5793344.4 | -0.05 , , , ST_SkewX Returns the georeference X skew (or rotation parameter) float8 ST_SkewX raster rast Returns the georeference X skew (or rotation parameter). Refer to World File for more details. SELECT rid, ST_SkewX(rast) As skewx, ST_SkewY(rast) As skewy, ST_GeoReference(rast) as georef FROM dummy_rast; rid | skewx | skewy | georef -----+-------+-------+-------------------- 1 | 0 | 0 | 2.0000000000 : 0.0000000000 : 0.0000000000 : 3.0000000000 : 0.5000000000 : 0.5000000000 : 2 | 0 | 0 | 0.0500000000 : 0.0000000000 : 0.0000000000 : -0.0500000000 : 3427927.7500000000 : 5793244.0000000000 , , ST_SkewY Returns the georeference Y skew (or rotation parameter) float8 ST_SkewY raster rast Returns the georeference Y skew (or rotation parameter). Refer to World File for more details. SELECT rid, ST_SkewX(rast) As skewx, ST_SkewY(rast) As skewy, ST_GeoReference(rast) as georef FROM dummy_rast; rid | skewx | skewy | georef -----+-------+-------+-------------------- 1 | 0 | 0 | 2.0000000000 : 0.0000000000 : 0.0000000000 : 3.0000000000 : 0.5000000000 : 0.5000000000 : 2 | 0 | 0 | 0.0500000000 : 0.0000000000 : 0.0000000000 : -0.0500000000 : 3427927.7500000000 : 5793244.0000000000 , , ST_SRID Returns the spatial reference identifier of the raster as defined in spatial_ref_sys table. integer ST_SRID raster rast Returns the spatial reference identifier of the raster object as defined in the spatial_ref_sys table. From PostGIS 2.0+ the srid of a non-georeferenced raster/geometry is 0 instead of the prior -1. SELECT ST_SRID(rast) As srid FROM dummy_rast WHERE rid=1; srid ---------------- 0 , ST_UpperLeftX Returns the upper left x coordinate of raster in projected spatial ref. float8 ST_UpperLeftX raster rast Returns the upper left x coordinate of raster in projected spatial ref. SELECt rid, ST_UpperLeftX(rast) As ulx FROM dummy_rast; rid | ulx -----+------------ 1 | 0.5 2 | 3427927.75 , , ST_UpperLeftY Returns the upper left y coordinate of raster in projected spatial ref. float8 ST_UpperLeftY raster rast Returns the upper left y coordinate of raster in projected spatial ref. SELECT rid, ST_UpperLeftY(rast) As uly FROM dummy_rast; rid | uly -----+--------- 1 | 0.5 2 | 5793244 , , ST_Width Returns the width of the raster in pixels? integer ST_Width raster rast Returns the width of the raster. SELECT ST_Width(rast) As rastwidth FROM dummy_rast WHERE rid=1; rastwidth ---------------- 10 ST_AddBand Returns a raster with the new band of given type added with given initial value raster ST_AddBand raster rast text pixeltype raster ST_AddBand raster rast text pixeltype double precision initialvalue raster ST_AddBand raster rast text pixeltype double precision initialvalue double precision nodataval raster ST_AddBand raster rast integer index text pixeltype raster ST_AddBand raster rast integer band_num text pixeltype double precision initialvalue raster ST_AddBand raster rast integer band_num text pixeltype double precision initialvalue double precision nodataval Returns a raster with a new band added in given position (band number), of given type, of given intial value, and of given nodata value. If no index is specified, the band is added to the end. Pixel type is a string representation of one of the pixel types specified in . If an existing index is specfied all subsequent bands >= that index are incremented by 1. If an initial value greater than the max of the pixel type is specified, then the initial value is set to the highest value allowed by the pixel type. -- Add another band of type 8 bit unsigned integer with pixels initialized to 200 UPDATE dummy_rast SET rast = ST_AddBand(rast,'8BUI',200) WHERE rid = 1; -- Create an empty raster 100x100 units, with upper left right at 0, add 2 bands (band 1 is 0/1 boolean bit switch, band2 allows values 0-15) INSERT INTO dummy_rast(rid,rast) VALUES(10, ST_AddBand(ST_AddBand(ST_MakeEmptyRaster(100,100,0,0,1,-1,0,0, -1), '1BB'), '4BUI') ); -- output meta data of raster bands to verify all is right -- SELECT (bmd).* FROM (SELECT ST_BandMetaData(rast,generate_series(1,2)) As bmd FROM dummy_rast WHERE rid = 10) AS foo; --result -- pixeltype | hasnodatavalue | nodatavalue | isoutdb | path -----------+----------------+-------------+---------+------ 1BB | f | 0 | f | 4BUI | f | 0 | f | -- output meta data of raster - SELECT (rmd).width, (rmd).height, (rmd).numbands FROM (SELECT ST_MetaData(rast) As rmd FROM dummy_rast WHERE rid = 10) AS foo; -- result -- upperleftx | upperlefty | width | height | pixelsizex | pixelsizey | skewx | skewy | srid | numbands ------------+------------+-------+--------+------------+------------+-------+-------+------+---------- 0 | 0 | 100 | 100 | 1 | -1 | 0 | 0 | -1 | 2 , , , , ST_BandHasNoDataValue Returns whether or not a band has a value that should be considered no data. If no band number provided 1 is assumed. boolean ST_BandHasNoDataValue raster rast boolean ST_BandHasNoDataValue raster rast integer bandnum Returns true or false whether or not a band has a value that should be considered no data. If no band number provided 1 is assumed. -- change just first band no data value SELECT ST_BandHasNoDataValue(rast,1) As hasnodataval FROM dummy_rast WHERE rid = 2; hasnodataval ------------ f ,, , ST_BandMetaData Returns basic meta data for a specific raster band. band num 1 is assumed if none-specified. record ST_BandMetaData raster rast record ST_BandMetaData raster rast integer bandnum Returns basic meta data about a raster band. Columns returned pixeltype | hasnodatavalue | nodatavalue | isoutdb | path. If raster contains no bands then an error is thrown. SELECT rid, (foo.md).* FROM (SELECT rid, ST_BandMetaData(rast,1) As md FROM dummy_rast WHERE rid=2) As foo; rid | pixeltype | hasnodatavalue | nodatavalue | isoutdb | path -----+-----------+----------------+-------------+---------+------ 2 | 8BUI | t | 0 | f | , ST_BandNoDataValue Returns the value in a given band that represents no data. If no band num 1 is assumed. integer ST_BandNoDataValue raster rast integer ST_BandNoDataValue raster rast integer bandnum Returns the value that represents no data for the band SELECT ST_BandNoDataValue(rast,1) As bnval1, ST_BandNoDataValue(rast,2) As bnval2, ST_BandNoDataValue(rast,3) As bnval3 FROM dummy_rast WHERE rid = 2; bnval1 | bnval2 | bnval3 --------+--------+-------- 0 | 0 | 0 ST_BandPath Returns system file path to a band stored in file system. If no bandnum specified, 1 is assumed. text ST_BandPath raster rast text ST_BandPath raster rast integer bandnum Returns system file path to a band. Throws an error if called with an in db band. ST_BandPixelType Returns the type of pixel for given band. If no bandnum specified, 1 is assumed. text ST_BandPixelType raster rast text ST_BandPixelType raster rast integer bandnum Returns the value that represents no data for the band There are 11 pixel types. Pixel Types supported are as follows: 1BB - 1-bit boolean 2BUI - 2-bit unsigned integer 4BUI - 4-bit unsigned integer 8BSI - 8-bit signed integer 8BUI - 8-bit unsigned integer 16BSI - 16-bit signed integer 16BUI - 16-bit unsigned integer 32BSI - 32-bit signed integer 32BUI - 32-bit unsigned integer 32BF - 32-bit float 64BF - 64-bit float SELECT ST_BandPixelType(rast,1) As btype1, ST_BandPixelType(rast,2) As btype2, ST_BandPixelType(rast,3) As btype3 FROM dummy_rast WHERE rid = 2; btype1 | btype2 | btype3 --------+--------+-------- 8BUI | 8BUI | 8BUI ST_PixelAsPolygon Returns the geometry that bounds the pixel (for now a rectangle) for a particular band, row, column. If no band specified band num 1 is assumed. geometry ST_PixelAsPolygon raster rast integer columnx integer rowy geometry ST_PixelAsPolygon raster rast integer bandnum integer columnx integer rowy Returns the geometry that bounds the pixel (for now a rectangle) for a particular band, row, column. If no band specified band num 1 is assumed. -- get raster pixel polygon SELECT i,j, ST_AsText(ST_PixelAsPolygon(foo.rast, i,j)) As b1pgeom FROM dummy_rast As foo CROSS JOIN generate_series(1,2) As i CROSS JOIN generate_series(1,1) As j WHERE rid=2; i | j | b1pgeom ---+---+----------------------------------------------------------------------------- 1 | 1 | POLYGON((3427927.75 5793244,3427927.8 5793244,3427927.8 5793243.95,... 2 | 1 | POLYGON((3427927.8 5793244,3427927.85 5793244,3427927.85 5793243.95, .. , , ST_Value Returns the value of a given band in a given columnx, rowy pixel or at a particular geometric point. Band numbers start at 1 and assumed to be 1 if not specified. double precision ST_Value raster rast geometry pt double precision ST_Value raster rast integer bandnum geometry pt double precision ST_Value raster rast integer columnx integer rowy double precision ST_Value raster rast integer bandnum integer columnx integer rowy Returns the value of a given band in a given columnx, rowy pixel. Band numbers start at 1. Note that although the X and Ys of these are not in coordinates of the spatial system, you can get that by the following relationship. Coordinate upper left ppoint of a row column is: ST_SetSRID(ST_Point(ST_UpperLeftX(rast) + ST_PixelSizeX(rast)*columnx, ST_UpperLeftY(rast) + ST_PixelSizeY(rast)*columny), ST_SRID(rast)) If you want the pixel box instead of the upper left point, you can use the ST_MakeEnvelope function and translate it every x,y. -- get raster values at particular postgis geometry points -- the srid of your geometry should be same as for your raster SELECT rid, ST_Value(rast, foo.pt_geom) As b1pval, ST_Value(rast, 2, foo.pt_geom) As b2pval FROM dummy_rast CROSS JOIN (SELECT ST_SetSRID(ST_Point(3427927.77,5793243.76),-1) As pt_geom) As foo WHERE rid=2; rid | b1pval | b2pval -----+--------+-------- 2 | 252 | 79 -- general fictitious example using a real table SELECT rid, ST_Value(rast, 3, sometable.geom) As b3pval FROM sometable WHERE ST_Intersects(rast,sometable.geom); SELECT rid, ST_Value(rast, 1,1,1) As b1pval, ST_Value(rast, 2,1,1) As b2pval, ST_Value(rast, 3,1,1) As b3pval FROM dummy_rast WHERE rid=2; rid | b1pval | b2pval | b3pval -----+--------+--------+-------- 2 | 253 | 78 | 70 --- Get all values in bands 1,2,3 of each pixel -- SELECT x, y, ST_Value(rast, 1, x, y) As b1val, ST_Value(rast, 2, x, y) As b2val, ST_Value(rast, 3, x, y) As b3val FROM dummy_rast CROSS JOIN generate_series(1,1000) As x CROSS JOIN generate_series(1,1000) As y WHERE rid = 2 AND x <= ST_Width(rast) AND y <= ST_Height(rast); x | y | b1val | b2val | b3val ---+---+-------+-------+------- 1 | 1 | 253 | 78 | 70 1 | 2 | 253 | 96 | 80 1 | 3 | 250 | 99 | 90 1 | 4 | 251 | 89 | 77 1 | 5 | 252 | 79 | 62 2 | 1 | 254 | 98 | 86 2 | 2 | 254 | 118 | 108 : : --- Get all values in bands 1,2,3 of each pixel same as above but returning the upper left point point of each pixel -- SELECT ST_AsText(ST_SetSRID( ST_Point(ST_UpperLeftX(rast) + ST_PixelSizeX(rast)*x, ST_UpperLeftY(rast) + ST_PixelSizeY(rast)*y), ST_SRID(rast))) As uplpt , ST_Value(rast, 1, x, y) As b1val, ST_Value(rast, 2, x, y) As b2val, ST_Value(rast, 3, x, y) As b3val FROM dummy_rast CROSS JOIN generate_series(1,1000) As x CROSS JOIN generate_series(1,1000) As y WHERE rid = 2 AND x <= ST_Width(rast) AND y <= ST_Height(rast); uplpt | b1val | b2val | b3val -----------------------------+-------+-------+------- POINT(3427929.25 5793245.5) | 253 | 78 | 70 POINT(3427929.25 5793247) | 253 | 96 | 80 POINT(3427929.25 5793248.5) | 250 | 99 | 90 : --- Get a polygon formed by union of all pixels that fall in a particular value range and intersect particular polygon -- SELECT ST_AsText(ST_Union(pixpolyg)) As shadow FROM (SELECT ST_Translate(ST_MakeEnvelope( ST_UpperLeftX(rast), ST_UpperLeftY(rast), ST_UpperLeftX(rast) + ST_PixelSizeX(rast), ST_UpperLeftY(rast) + ST_PixelSizeY(rast), 0 ), ST_PixelSizeX(rast)*x, ST_PixelSizeY(rast)*y ) As pixpolyg, ST_Value(rast, 2, x, y) As b2val FROM dummy_rast CROSS JOIN generate_series(1,1000) As x CROSS JOIN generate_series(1,1000) As y WHERE rid = 2 AND x <= ST_Width(rast) AND y <= ST_Height(rast)) As foo WHERE ST_Intersects( pixpolyg, ST_GeomFromText('POLYGON((3427928 5793244,3427927.75 5793243.75,3427928 5793243.75,3427928 5793244))',0) ) AND b2val != 254; shadow ------------------------------------------------------------------------------------ MULTIPOLYGON(((3427928 5793243.9,3427928 5793243.85,3427927.95 5793243.85,3427927.95 5793243.9, 3427927.95 5793243.95,3427928 5793243.95,3427928.05 5793243.95,3427928.05 5793243.9,3427928 5793243.9)),((3427927.95 5793243.9,3427927.95 579324 3.85,3427927.9 5793243.85,3427927.85 5793243.85,3427927.85 5793243.9,3427927.9 5793243.9,3427927.9 5793243.95, 3427927.95 5793243.95,3427927.95 5793243.9)),((3427927.85 5793243.75,3427927.85 5793243.7,3427927.8 5793243.7,3427927.8 5793243.75 ,3427927.8 5793243.8,3427927.8 5793243.85,3427927.85 5793243.85,3427927.85 5793243.8,3427927.85 5793243.75)), ((3427928.05 5793243.75,3427928.05 5793243.7,3427928 5793243.7,3427927.95 5793243.7,3427927.95 5793243.75,3427927.95 5793243.8,3427 927.95 5793243.85,3427928 5793243.85,3427928 5793243.8,3427928.05 5793243.8, 3427928.05 5793243.75)),((3427927.95 5793243.75,3427927.95 5793243.7,3427927.9 5793243.7,3427927.85 5793243.7, 3427927.85 5793243.75,3427927.85 5793243.8,3427927.85 5793243.85,3427927.9 5793243.85, 3427927.95 5793243.85,3427927.95 5793243.8,3427927.95 5793243.75))) --- Checking all the pixels of a large raster tile can take a long time. --- You can dramatically improve speed at some lose of precision by orders of magnitude -- by sampling pixels using the step optional parameter of generate_series. -- This next example does the same as previous but by checking 1 for every 4 (2x2) pixels and putting in the last checked -- putting in the checked pixel as the value for subsequent 4 SELECT ST_AsText(ST_Union(pixpolyg)) As shadow FROM (SELECT ST_Translate(ST_MakeEnvelope( ST_UpperLeftX(rast), ST_UpperLeftY(rast), ST_UpperLeftX(rast) + ST_PixelSizeX(rast)*2, ST_UpperLeftY(rast) + ST_PixelSizeY(rast)*2, 0 ), ST_PixelSizeX(rast)*x, ST_PixelSizeY(rast)*y ) As pixpolyg, ST_Value(rast, 2, x, y) As b2val FROM dummy_rast CROSS JOIN generate_series(1,1000,2) As x CROSS JOIN generate_series(1,1000,2) As y WHERE rid = 2 AND x <= ST_Width(rast) AND y <= ST_Height(rast) ) As foo WHERE ST_Intersects( pixpolyg, ST_GeomFromText('POLYGON((3427928 5793244,3427927.75 5793243.75,3427928 5793243.75,3427928 5793244))',0) ) AND b2val != 254; shadow ------------------------------------------------------------------------------------ MULTIPOLYGON(((3427927.9 5793243.85,3427927.8 5793243.85,3427927.8 5793243.95, 3427927.9 5793243.95,3427928 5793243.95,3427928.1 5793243.95,3427928.1 5793243.85,3427928 5793243.85,3427927.9 5793243.85)), ((3427927.9 5793243.65,3427927.8 5793243.65,3427927.8 5793243.75,3427927.8 5793243.85,3427927.9 5793243.85, 3427928 5793243.85,3427928 5793243.75,3427928.1 5793243.75,3427928.1 5793243.65,3427928 5793243.65,3427927.9 5793243.65))) , , , , , , , , , , , , ST_SetValue Sets the value of a given band in a given columnx, rowy pixel or at a pixel that intersects a particular geometric point. Band numbers start at 1 and assumed to be 1 if not specified. double precision ST_SetValue raster rast geometry pt double precision newvalue double precision ST_SEtValue raster rast integer bandnum geometry pt double precision newvalue double precision ST_SetValue raster rast integer columnx integer rowy double precision newvalue double precision ST_SetValue raster rast integer bandnum integer columnx integer rowy double precision newvalue Sets the specified pixel value to new value for the designed band given the row column location or a goemetric point location. If no band is specified, then band 1 is assumed. Setting by geometry currently only works for points. -- Geometry example SELECT (foo.geomval).val, ST_AsText(ST_Union((foo.geomval).geom)) FROM (SELECT ST_DumpAsPolygons( ST_SetValue(rast,1, ST_Point(3427927.75, 5793243.95), 50) ) As geomval FROM dummy_rast where rid = 2) As foo WHERE (foo.geomval).val < 250 GROUP BY (foo.geomval).val; val | st_astext -----+------------------------------------------------------------------- 50 | POLYGON((3427927.75 5793244,3427927.75 5793243.95,3427927.8 579324 ... 249 | POLYGON((3427927.95 5793243.95,3427927.95 5793243.85,3427928 57932 ... , ST_SetGeoReference Set Georefence 6 georeference parameters in a single call. Numbers should be separated by white space. Accepts inputs in GDAL or ESRI format. Default is GDAL. raster ST_SetGeoReference raster rast text georefcoords raster ST_SetGeoReference raster rast text georefcoords text format Set Georefence 6 georeference parameters in a single call. Accepts inputs in 'GDAL' or 'ESRI' format. Default is GDAL. If 6 coordinates are not provided will return null. Difference between format representations is as follows: GDAL: pixelsizex skewy skewx pixelsizey upperleftx upperlefty ESRI: pixelsizex skewy skewx pixelsizey upperleftx + pixelsizex*0.5 upperlefty + pixelsizey*0.5 UPDATE dummy_rast SET rast = ST_SetGeoReference(rast, '2 0 0 3 0.5 0.5','GDAL') WHERE rid=1; -- same coordinates set in 'ESRI' format UPDATE dummy_rast SET rast = ST_SetGeoReference(rast, '2 0 0 3 1.5 2','ESRI') WHERE rid=1; , , , , ST_SetPixelSize Sets the x and y size of pixels in units of coordinate reference system. Number units/pixel width/height raster ST_SetPixelSize raster rast float8 xy raster ST_SetPixelSize raster rast float8 x float8 y Sets the x and y size of pixels in units of coordinate reference system. Number units/pixel width/height. If only one unit passed in, assumed x and y are the same number. UPDATE dummy_rast SET rast = ST_SetPixelSize(rast,1.5) WHERE rid = 2; SELECT ST_PixelSizeX(rast) As pixx, ST_PixelSizeY(rast) As pixy, ST_Box2D(rast) As newbox FROM dummy_rast WHERE rid = 2; pixx | pixy | newbox ------+------+---------------------------------------------- 1.5 | 1.5 | BOX(3427927.75 5793244,3427935.25 5793251.5) UPDATE dummy_rast SET rast = ST_SetPixelSize(rast,1.5,0.55) WHERE rid = 2; SELECT ST_PixelSizeX(rast) As pixx, ST_PixelSizeY(rast) As pixy, ST_Box2D(rast) As newbox FROM dummy_rast WHERE rid = 2; pixx | pixy | newbox ------+------+-------------------------------------------- 1.5 | 0.55 | BOX(3427927.75 5793244,3427935.25 5793247) , , ST_SetSkew Sets the georeference X and Y skew (or rotation parameter). If only one is passed in sets x and y to same number. raster ST_SetSkew raster rast float8 skewxy raster ST_SetSkew raster rast float8 skewx float8 skewy Sets the georeference X and Y skew (or rotation parameter). If only one is passed in sets x and y to same number. Refer to World File for more details. -- Example 1 UPDATE dummy_rast SET rast = ST_SetSkew(rast,1,2) WHERE rid = 1; SELECT rid, ST_SkewX(rast) As skewx, ST_SkewY(rast) As skewy, ST_GeoReference(rast) as georef FROM dummy_rast WHERE rid = 1; rid | skewx | skewy | georef ----+-------+-------+-------------- 1 | 1 | 2 | 2.0000000000 : 2.0000000000 : 1.0000000000 : 3.0000000000 : 0.5000000000 : 0.5000000000 -- Example 2 set both to same number: UPDATE dummy_rast SET rast = ST_SetSkew(rast,0) WHERE rid = 1; SELECT rid, ST_SkewX(rast) As skewx, ST_SkewY(rast) As skewy, ST_GeoReference(rast) as georef FROM dummy_rast WHERE rid = 1; rid | skewx | skewy | georef -----+-------+-------+-------------- 1 | 0 | 0 | 2.0000000000 : 0.0000000000 : 0.0000000000 : 3.0000000000 : 0.5000000000 : 0.5000000000 ,, , ST_SetSRID Sets the SRID of a raster to a particular integer srid defined in the spatial_ref_sys table. raster ST_SetSRID raster rast integer srid Sets the SRID on a raster to a particular integer value. This function does not transform the raster in any way - it simply sets meta data defining the spatial ref of the coordinate reference system that it's currently in. Useful for transformations later. , ST_SetUpperLeft Sets the value of the upper left corner of the pixel to projected x,y coordinates raster ST_SetUpperLeft raster rast double precision x double precision y Set the value of the uppler left corner of raster to the projected x coordinates SELECT ST_SetUpperLeft(rast,-71.01,42.37) FROM dummy_rast WHERE rid = 2; , ST_SetBandHasNoDataValue Sets whether or not a band has a value that should be considered no data. raster ST_SetBandHasNoDataValue raster rast integer bandnum boolean has_nodatavalue Sets whether or not a band has a value that should be considered no data. -- change just first band no data value UPDATE dummy_rast SET rast = ST_SetBandHasNoDataValue(rast,1, false) WHERE rid = 2; , ST_SetBandNoDataValue Sets the value for the given band that represents no data. integer ST_SetBandNoDataValue raster rast integer bandnum double precision val Sets the value that represents no data for the band. This will effect and results. -- change just first band no data value UPDATE dummy_rast SET rast = ST_SetBandNoDataValue(rast,1, 254) WHERE rid = 2; -- change no data band value of bands 1,2,3 UPDATE dummy_rast SET rast = ST_SetBandNoDataValue( ST_SetBandNoDataValue( ST_SetBandNoDataValue( rast,1, 254) ,2,99), 3,108) WHERE rid = 2; , ST_AsBinary Return the Well-Known Binary (WKB) representation of the raster without SRID meta data. bytea ST_AsBinary raster rast Returns the Binary representation of the raster. There are 2 variants of the function. The first variant takes no endian encoding paramater and defaults to little endian. The second variant takes a second argument denoting the encoding - using little-endian ('NDR') or big-endian ('XDR') encoding. This is useful in binary cursors to pull data out of the database without converting it to a string representation. SELECT ST_AsBinary(rast) As rastbin FROM dummy_rast WHERE rid=1; rastbin --------------------------------------------------------------------------------- \001\000\000\000\000\000\000\000\000\000\000\000@\000\000\000\000\000\000\010@\ 000\000\000\000\000\000\340?\000\000\000\000\000\000\340?\000\000\000\000\000\00 0\000\000\000\000\000\000\000\000\000\000\012\000\000\000\012\000\024\000 ST_Box2D Returns the box 2d representation of the enclosing box of the raster box2d ST_Box2D raster rast Returns the box representing the extent of the raster. The polygon is defined by the corner points of the bounding box ((MINX, MINY), (MAXX, MAXY)) SELECT rid, ST_Box2D(rast) As rastbox FROM dummy_rast; rid | rastbox ----+------------------------------------------------- 1 | BOX(0.5 0.5,20.5 60.5) 2 | BOX(3427927.75 5793243.5,3427928 5793244) ST_ConvexHull Return the convex hull geometry of the raster including pixel values equal to BandNoDataValue. For regular shaped and non-skewed rasters, this gives the same answer as ST_Envelope so only useful for irregularly shaped or skewed rasters. geometry ST_ConvexHull raster rast Return the convex hull geometry of the raster including the NoDataBandValue band pixels. For regular shaped and non-skewed rasters, this gives more or less the same answer as ST_Envelope so only useful for irregularly shaped or skewed rasters. ST_Envelope floors the coordinates and hence add a little buffer around the raster so the answer is subtley different from ST_ConvexHull which does not floor. Refer to PostGIS Raster Specification for a diagram of this. -- Note envelope and convexhull are more or less the same SELECT ST_AsText(ST_ConvexHull(rast)) As convhull, ST_AsText(ST_Envelope(rast)) As env FROM dummy_rast WHERE rid=1; convhull | env --------------------------------------------------------+----------------------- POLYGON((0.5 0.5,20.5 0.5,20.5 60.5,0.5 60.5,0.5 0.5)) | POLYGON((0 0,20 0,20 60,0 60,0 0)) -- now we skew the raster -- note how the convex hull and envelope are now different SELECT ST_AsText(ST_ConvexHull(rast)) As convhull, ST_AsText(ST_Envelope(rast)) As env FROM (SELECT ST_SetRotation(rast,0.1,0.1) As rast FROM dummy_rast WHERE rid=1) As foo; convhull | env --------------------------------------------------------+------------------------------------ POLYGON((0.5 0.5,20.5 1.5,22.5 61.5,2.5 60.5,0.5 0.5)) | POLYGON((0 0,22 0,22 61,0 61,0 0)) , , ST_DumpAsPolygons Returns a set of geomval (geom,val) rows, from a given raster band. If no band number is specified, band num defaults to 1. setof geomval ST_DumpAsPolygons raster rast setof geomval ST_DumpAsPolygons raster rast integer band_num This is a set-returning function (SRF). It returns a set of geomval rows, formed by a geometry (geom) and a pixel band value (val). Each polygon is the union of all pixels for that band that have the same pixel value denoted by val. ST_DumpAsPolygon is useful for polygonizing rasters. It is the reverse of a GROUP BY in that it creates new rows. For example it can be used to expand a single raster into multiple POLYGONS/MULTIPOLYGONS. Availability: Requires GDAL 1.7 or higher. If there is a no data value set for a band, pixels with that value will not be returned. SELECT val, ST_AsText(geom) As geomwkt FROM ( SELECT (ST_DumpAsPolygons(rast)).* FROM dummy_rast WHERE rid = 2 ) As foo WHERE val BETWEEN 249 and 251 ORDER BY val; val | geomwkt -----+-------------------------------------------------------------------------- 249 | POLYGON((3427927.95 5793243.95,3427927.95 5793243.85,3427928 5793243.85, 3427928 5793243.95,3427927.95 5793243.95)) 250 | POLYGON((3427927.75 5793243.9,3427927.75 5793243.85,3427927.8 5793243.85, 3427927.8 5793243.9,3427927.75 5793243.9)) 250 | POLYGON((3427927.8 5793243.8,3427927.8 5793243.75,3427927.85 5793243.75, 3427927.85 5793243.8, 3427927.8 5793243.8)) 251 | POLYGON((3427927.75 5793243.85,3427927.75 5793243.8,3427927.8 5793243.8, 3427927.8 5793243.85,3427927.75 5793243.85)) , ST_Envelope Returns the polygon representation of the extent of the raster. geometry ST_Envelope raster rast Returns the polygon representation of the extent of the raster in spatial coordinate units defiend by srid. It is a float8 minimum bounding box represented as a polygon. The polygon is defined by the corner points of the bounding box ((MINX, MINY), (MINX, MAXY), (MAXX, MAXY), (MAXX, MINY), (MINX, MINY)) SELECT rid, ST_AsText(ST_Envelope(rast)) As envgeomwkt FROM dummy_rast; rid | envgeomwkt -----+-------------------------------------------------------------------- 1 | POLYGON((0 0,20 0,20 60,0 60,0 0)) 2 | POLYGON((3427927 5793243,3427928 5793243, 3427928 5793244,3427927 5793244, 3427927 5793243)) , , ST_Intersection Returns a set of geometry-pixelvalue pairs resulting from intersection of a raster band with a geometry. If no band number is specified, band 1 is assumed. setof geomval ST_Intersection geometry geom raster rast setof geomval ST_Intersection geometry geom raster rast integer band_num setof geomval ST_Intersection raster rast geometry geom setof geomval ST_Intersection raster rast integer band_num geometry geom Return the intersections of the geometry with the vectorized parts of the raster and the values associated with those parts, if really their intersection is not empty. If no band number is specified band 1 is assumed. SELECT foo.rid, foo.gid, ST_AsText((foo.geomval).geom) As geomwkt, (foo.geomval).val FROM ( SELECT A.rid, g.gid , ST_Intersection(A.rast, g.geom) As geomval FROM dummy_rast AS A CROSS JOIN (VALUES (1, ST_Point(3427928, 5793243.85) ) , (2, ST_GeomFromText('LINESTRING(3427927.85 5793243.75,3427927.8 5793243.75,3427927.8 5793243.8)') ), (3, ST_GeomFromText('LINESTRING(1 2, 3 4)') ) ) As g(gid,geom) WHERE A.rid =2 ) As foo; rid | gid | geomwkt | val -----+-----+--------------------------------------------------------------------------------------------- 2 | 1 | POINT(3427928 5793243.85) | 249 2 | 1 | POINT(3427928 5793243.85) | 253 2 | 2 | POINT(3427927.85 5793243.75) | 254 2 | 2 | POINT(3427927.8 5793243.8) | 251 2 | 2 | POINT(3427927.8 5793243.8) | 253 2 | 2 | LINESTRING(3427927.8 5793243.75,3427927.8 5793243.8) | 252 2 | 2 | MULTILINESTRING((3427927.8 5793243.8,3427927.8 5793243.75),...) | 250 2 | 3 | GEOMETRYCOLLECTION EMPTY , ST_Polygon Returns a polygon geometry formed by the union of pixels that have a pixel value that is not no data value. If no band number is specified, band num defaults to 1. geometry ST_Polygon raster rast geometry ST_Polygon raster rast integer band_num Availability: Requires GDAL 1.7 or higher. -- by default no data band value is 0 or not set, so polygon will return a square polygon SELECT ST_AsText(ST_Polygon(rast)) As geomwkt FROM dummy_rast WHERE rid = 2; geomwkt -------------------------------------------- POLYGON((3427927.8 5793243.75,3427927.75 5793243.75,3427927.75 5793243.8,3427927.75 5793243.85,3427927.75 5793243.9, 3427927.75 5793244,3427927.8 5793244,3427927.85 5793244,3427927.9 5793244,3427928 5793244,3427928 5793243.95, 3427928 5793243.85,3427928 5793243.8,3427928 5793243.75,3427927.85 5793243.75,3427927.8 5793243.75)) -- now we change the no data value of first band UPDATE dummy_rast SET rast = ST_SetBandNoDataValue(rast,1,254) WHERE rid = 2; SELECt rid, ST_BandNoDataValue(rast) from dummy_rast where rid = 2; -- ST_Polygon excludes the pixel value 254 and returns a multipolygon SELECT ST_AsText(ST_Polygon(rast)) As geomwkt FROM dummy_rast WHERE rid = 2; geomwkt --------------------------------------------------------- MULTIPOLYGON(((3427927.9 5793243.95,3427927.85 5793243.95,3427927.85 5793244,3427927.9 5793244,3427927.9 5793243.95)), ((3427928 5793243.85,3427928 5793243.8,3427927.95 5793243.8,3427927.95 5793243.85,3427927.9 5793243.85,3427927.9 5793243.9,3427927.9 5793243.95,3427927.95 5793243.95,3427928 5793243.95,3427928 5793243.85)), ((3427927.8 5793243.75,3427927.75 5793243.75,3427927.75 5793243.8,3427927.75 5793243.85,3427927.75 5793243.9,3427927.75 5793244,3427927.8 5793244, 3427927.8 5793243.9,3427927.8 5793243.85,3427927.85 5793243.85,3427927.85 5793243.8,3427927.85 5793243.75,3427927.8 5793243.75))) -- Or if you want the no data value different for just one time SELECT ST_AsText( ST_Polygon( ST_SetBandNoDataValue(rast,1,252) ) ) As geomwkt FROM dummy_rast WHERE rid =2; geomwkt --------------------------------- POLYGON((3427928 5793243.85,3427928 5793243.8,3427928 5793243.75,3427927.85 5793243.75,3427927.8 5793243.75,3427927.8 5793243.8,3427927.75 5793243.8,3427927.75 5793243.85,3427927.75 5793243.9,3427927.75 5793244,3427927.8 5793244,3427927.85 5793244,3427927.9 5793244,3427928 5793244,3427928 5793243.95,3427928 5793243.85), (3427927.9 5793243.9,3427927.9 5793243.85,3427927.95 5793243.85,3427927.95 5793243.9,3427927.9 5793243.9)) , && Returns TRUE if A's bounding box overlaps B's. boolean && raster A raster B The && operator returns TRUE if the bounding box of raster A overlaps the bounding box of raster B. This operand will make use of any indexes that may be available on the rasters. SELECT A.rid As a_rid, B.rid As b_rid, A.rast && B.rast As overlap FROM dummy_rast AS A CROSS JOIN dummy_rast AS B LIMIT 3; a_rid | b_rid | overlap -------+-------+--------- 2 | 2 | t 2 | 3 | f 2 | 1 | f &< Returns TRUE if A's bounding box is to the left of B's. boolean &< raster A raster B The &< operator returns TRUE if the bounding box of raster A overlaps or is to the left of the bounding box of raster B, or more accurately, overlaps or is NOT to the right of the bounding box of raster B. This operand will make use of any indexes that may be available on the geometries. SELECT A.rid As a_rid, B.rid As b_rid, A.rast &< B.rast As overleft FROM dummy_rast AS A CROSS JOIN dummy_rast AS B; a_rid | b_rid | overleft ------+-------+---------- 2 | 2 | t 2 | 3 | f 2 | 1 | f 3 | 2 | t 3 | 3 | t 3 | 1 | f 1 | 2 | t 1 | 3 | t 1 | 1 | t &< Returns TRUE if A's bounding box is to the right of B's. boolean &> raster A raster B The &< operator returns TRUE if the bounding box of raster A overlaps or is to the right of the bounding box of raster B, or more accurately, overlaps or is NOT to the left of the bounding box of raster B. This operand will make use of any indexes that may be available on the geometries. SELECT A.rid As a_rid, B.rid As b_rid, A.rast &> B.rast As overright FROM dummy_rast AS A CROSS JOIN dummy_rast AS B; a_rid | b_rid | overright -------+-------+---------- 2 | 2 | t 2 | 3 | t 2 | 1 | t 3 | 2 | f 3 | 3 | t 3 | 1 | f 1 | 2 | f 1 | 3 | t 1 | 1 | t ST_Intersects Returns TRUE if rastA pixel in a band with non-no data band value intersects with a geometry/raster. If band number is not specified it defaults to 1. boolean ST_Intersects raster rastA geometry geomB boolean ST_Intersects raster rastA integer band_num geometry geomB boolean ST_Intersects geometry geomA raster rastB boolean ST_Intersects geometry geomA raster rastB integer band_num Returns true if any pixel in a raster band has a value that is not nodatavalue and that geometry region of the pixel intersects the geometry This operand will make use of any indexes that may be available on the geometries / rasters. SELECT A.rid, g.gid , ST_Intersects(A.rast, g.geom) As inter FROM dummy_rast AS A CROSS JOIN (VALUES (1, ST_Point(3427928, 5793243.85) ) , (2, ST_GeomFromText('LINESTRING(3427927.85 5793243.75,3427927.8 5793243.75,3427927.8 5793243.8)') ), (3, ST_GeomFromText('LINESTRING(1 2, 3 4)') ) ) As g(gid,geom) WHERE A.rid =2 ; rid | gid | inter -----+-----+------- 2 | 1 | t 2 | 2 | t 2 | 3 | f